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URN etd-0513111-155732
Author Po-Han Chen
Author's Email Address No Public.
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Department Applied Mathematics
Year 2010
Semester 2
Degree Master
Type of Document
Language English
Title λ-Toeplitz operators with analytic symbols
Date of Defense 2011-01-14
Page Count 14
Keyword
  • composition operators
  • Toeplitz operators
  • Abstract Let λ be a complex number in the closed unit disk D , And H be a separable Hilbert space with the orthonormal basis , say ,ε= {e_n:n=0,1,2,…}. A bounded operator T on H is called a λ- Toeplitz operator if <Te_(n+1) ,e_(m+1) >=λ<Te_n ,e_m > (where < , > is inner product on H) The L^2 function φ~ Σa_n e^inθ with a_n=<Te_0 ,e_n> for n>=0 , and a_n=<Te_n ,e_0 > for n<0 is , on the other hand , called the symbol of T The subject arises naturally from a special case of the operator equation
    S^* AS=λA+B where S is a shift on H ,
    which plays an essential role in finding bounded matrix (a_ij ) on L^2 (Z) that solves the system of equations
    {((a_(2i,2j)     =p_ij+aa_ij@a_(2i,2j-1)   =q_ij+ba_ij )@a_(2i-1,2j)  =ν_ij+ca_ij@a_(2i-1,2j-1) =ω_ij+da_ij )  ┤,
    for all i ,j belong Z , where (p_ij ) ,(q_ij ) ,(ν_ij ) ,(ω_ij ) are bounded matrices on l^2 (Z) and a ,b ,c ,d belong C . It is also clear that the well-known Toeplitz operators are precisely the solutions of S^* AS=A , when S is the unilateral shift . In this paper , we will determine the spectra of λ- Toeplitz operators with |λ|=1 of finite order, and when the symbols are analytic with C^1 boundary values.
    Advisory Committee
  • Chia-Hsin Liu - chair
  • Jyh-Shyang Jeang - co-chair
  • Hwa-Long Gau - co-chair
  • Mark C. Ho - advisor
  • Files
  • etd-0513111-155732.pdf
  • indicate in-campus access only
    Date of Submission 2011-05-13

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